A367261 G.f. satisfies A(x) = 1 + x*A(x) * (1 + x*A(x)^2)^3.

1, 1, 4, 16, 77, 393, 2113, 11761, 67217, 392140, 2325691, 13980390, 84990482, 521623164, 3227679457, 20114056545, 126125100615, 795207084713, 5038166859565, 32059491655921, 204806561028553, 1313023485343009, 8445060537757367, 54476991669555231

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

If g.f. satisfies A(x) = 1 + x*A(x)^t * (1 + x*A(x)^u)^s, then a(n) = Sum_{k=0..n} binomial(t*k+u*(n-k)+1,k) * binomial(s*k,n-k) / (t*k+u*(n-k)+1).

Prog

(PARI) a(n, s=3, t=1, u=2) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+1));

Crossrefs

Cf. A137953, A367239.

Sequence in context: A345889 A057725 A196192 * A364474 A159926 A020051

Adjacent sequences: A367258 A367259 A367260 * A367262 A367263 A367264

Keyword

nonn

Author

Seiichi Manyama, Nov 11 2023

Status

approved